Question

6 multiple choice 2 points the footlights of a stage have 12 red bulbs, 8 blue bulbs, and 10 yellow bulbs. if all the bulbs are expected to last the same amount of time, what is the probability that a yellow bulb will burn out first? 20/30 1/30 10/30 1 7 multiple choice 2 points mindy wanted to have a different sandwich each day for lunch. each sandwich would have one bread, one meat, and one cheese. she listed the types of bread, the sandwich meats, and the kinds of cheese in the chart below. sandwich fixings bread white whole wheat meat ham turkey cheese cheddar swiss how many different kinds of sandwiches can mindy make? 16 8 2 6

Explanation:

Step1: Calculate total number of bulbs

$12 + 8+10=30$

Step2: Calculate probability of yellow - bulb burning out first

The probability $P$ of an event is the number of favorable outcomes divided by the total number of outcomes. The number of yellow bulbs is 10 and the total number of bulbs is 30. So $P=\frac{10}{30}$

Use the counting principle. The number of ways to make a sandwich is the product of the number of choices for each component.

Step1: Identify number of choices for each component

Number of bread - choices: 2 (white, whole wheat)
Number of meat - choices: 2 (ham, turkey)
Number of cheese - choices: 2 (cheddar, swiss)

Step2: Calculate total number of sandwich combinations

By the counting principle, the total number of different sandwiches is $2\times2\times2 = 8$

Answer:

The probability that a yellow bulb will burn out first is $\frac{10}{30}$, so the answer for question 6 is C. $\frac{10}{30}$